Precise loop timing in Python

Question

For this project I'm designing a sequencer/drummachine that should be able to send MIDI notes with a precise tempo. Example: 16 notes per 2 seconds (i.e. in music terminology sixteen 1/16-notes per bar at BPM 120), i.e. one note every 125 milliseconds.

I'm thinking about:

import time

def midi_note_send(...):
    ...

while True:
    midi_note_send(...)
    time.sleep(0.125)

If I do like this, how to be sure it will be exactly 125 milliseconds? Isn't there a risk that 1000 iterations of this loop will be using 126 seconds instead of 125 seconds? If so, how to have a more precise loop?

Final note: a good drummachine should be able to keep a 120 BPM rythm during 1 hour, with a precision error < 1 second.
Used platform: Linux + RaspberryPi but this question is valid in general.

Answer 1

As I showed here

import time
def drummer():
    counter = 0
    # time.sleep(time.time() * 8 % 1 / 8) # enable to sync clock for demo
    while counter < 60 * 8:
        counter += 1
        print time.time()
        time.sleep(.125 - time.time() * 8 % 1 / 8)

This timer adjusts every beat and realigns.

And the adjustment takes almost no time:

timeit.timeit("time.time() * 8 % 1 / 8", number=1000000)
0.2493131160736084

which means every time it does that it takes about 0.25 microseconds

and for accuracy:

1488490895.000160
1488490895.125177
1488490895.250167
1488490895.375151
1488490895.500166
1488490895.625179
1488490895.750178
1488490895.875153

~28 microseconds of drift between notes. Running it locally for a longer time yields ~130μs of total drift (+- 65μs), but, as it syncs to the clock every beat, it won't deviate over time.